Positron emission tomography (PET) is undergoing a period of tremendous growth, and the continued development of new tracers and applications for oncology, cardiology, and neurology ensures that this modality will expand for many years to come. Technological advances are pushing PET toward fully-3D imaging with advanced statistical-based reconstruction algorithms. There is a significant need for improved iterative algorithms which are fast enough for routine use with fully-3D PET, and which take the guesswork out of choosing reconstruction parameters and regularization schemes. The objective of this project is to investigate new paradigms for statistical PET reconstruction which are specifically targeted and separately optimized for estimation and detection tasks. Two (2) complementary reconstruction frameworks are proposed: (Aim 1) direct reconstruction from raw LOR histograms using comprehensive modeling of the system transfer matrix, which achieves true maximum-likelihood estimation with exact Poisson statistics to produce lower-noise, higher spatial resolution images; and (Aim 2) statistically-regulated expectation-maximization (StatREM) algorithms, which adapt to the statistical quality of the dataset being reconstructed. The StatREM framework provides a means for selecting subsets and acceleration in a statistically-meaningful way, offering more robust acceleration than current algorithms. It also provides an iterative stopping criterion which may be optimized specifically for estimation and detection tasks. Moreover, StatREM provides spatially-adaptive regularizations which offer high resolution for high statistics regions, while at the same time regularizing low count background regions. We hypothesize that StatREM provides better lesion detection performance than current algorithms. Aims 3 and 4 will evaluate in detail the quantitation and lesion detection performance, respectively, of the new algorithms using experimentally acquired data of a highly-reproducible whole-body phantom. Each algorithm will be optimized with respect to these tasks. Lesion detectability will be evaluated using a detailed human observer study with a multi-slice display and localization receiver operating characteristic (LROC) analysis. The improvements in image quality offered by this research will broadly impact all applications of PET imaging, with specific benefit for tumor detection and quantitation.